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<font color='#009900'>// Copyright (C) 2012  Davis E. King (davis@dlib.net)
</font><font color='#009900'>// License: Boost Software License   See LICENSE.txt for the full license.
</font><font color='#0000FF'>#ifndef</font> DLIB_RLs_Hh_
<font color='#0000FF'>#define</font> DLIB_RLs_Hh_

<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='rls_abstract.h.html'>rls_abstract.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../matrix.h.html'>../matrix.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='function.h.html'>function.h</a>"

<font color='#0000FF'>namespace</font> dlib
<b>{</b>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='rls'></a>rls</b>
    <b>{</b>

    <font color='#0000FF'>public</font>:


        <font color='#0000FF'>explicit</font> <b><a name='rls'></a>rls</b><font face='Lucida Console'>(</font>
            <font color='#0000FF'><u>double</u></font> forget_factor_,
            <font color='#0000FF'><u>double</u></font> C_ <font color='#5555FF'>=</font> <font color='#979000'>1000</font>
        <font face='Lucida Console'>)</font>
        <b>{</b>
            <font color='#009900'>// make sure requires clause is not broken
</font>            <font color='#BB00BB'>DLIB_ASSERT</font><font face='Lucida Console'>(</font><font color='#979000'>0</font> <font color='#5555FF'>&lt;</font> forget_factor_ <font color='#5555FF'>&amp;</font><font color='#5555FF'>&amp;</font> forget_factor_ <font color='#5555FF'>&lt;</font><font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>&amp;</font><font color='#5555FF'>&amp;</font>
                        <font color='#979000'>0</font> <font color='#5555FF'>&lt;</font> C_,
                "<font color='#CC0000'>\t rls::rls()</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t invalid arguments were given to this function</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t forget_factor_: </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> forget_factor_ 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t C_:   </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> C_ 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t this: </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#0000FF'>this</font>
                <font face='Lucida Console'>)</font>;


            C <font color='#5555FF'>=</font> C_;
            forget_factor <font color='#5555FF'>=</font> forget_factor_;
        <b>}</b>

        <b><a name='rls'></a>rls</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>
        <b>{</b>
            C <font color='#5555FF'>=</font> <font color='#979000'>1000</font>;
            forget_factor <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
        <b>}</b>

        <font color='#0000FF'><u>double</u></font> <b><a name='get_c'></a>get_c</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
        <b>{</b>
            <font color='#0000FF'>return</font> C;
        <b>}</b>

        <font color='#0000FF'><u>double</u></font> <b><a name='get_forget_factor'></a>get_forget_factor</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
        <b>{</b>
            <font color='#0000FF'>return</font> forget_factor;
        <b>}</b>

        <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> EXP<font color='#5555FF'>&gt;</font>
        <font color='#0000FF'><u>void</u></font> <b><a name='train'></a>train</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> matrix_exp<font color='#5555FF'>&lt;</font>EXP<font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> x,
            <font color='#0000FF'><u>double</u></font> y
        <font face='Lucida Console'>)</font>
        <b>{</b>
            <font color='#009900'>// make sure requires clause is not broken
</font>            <font color='#BB00BB'>DLIB_ASSERT</font><font face='Lucida Console'>(</font><font color='#BB00BB'>is_col_vector</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font> <font color='#5555FF'>&amp;</font><font color='#5555FF'>&amp;</font>
                        <font face='Lucida Console'>(</font><font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font> <font color='#5555FF'>|</font><font color='#5555FF'>|</font> <font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>,
                "<font color='#CC0000'>\t void rls::train()</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t invalid arguments were given to this function</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t is_col_vector(x): </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#BB00BB'>is_col_vector</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t x.size():         </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t get_w().size():   </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t this: </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#0000FF'>this</font>
                <font face='Lucida Console'>)</font>;

            <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>R.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
            <b>{</b>
                R <font color='#5555FF'>=</font> identity_matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font face='Lucida Console'>(</font>x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font><font color='#5555FF'>*</font>C;
                w.<font color='#BB00BB'>set_size</font><font face='Lucida Console'>(</font>x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;
                w <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
            <b>}</b>

            <font color='#009900'>// multiply by forget factor and incorporate x*trans(x) into R.
</font>            <font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font> l <font color='#5555FF'>=</font> <font color='#979000'>1.0</font><font color='#5555FF'>/</font>forget_factor;
            <font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font> temp <font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>+</font> l<font color='#5555FF'>*</font><font color='#BB00BB'>trans</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font><font color='#5555FF'>*</font>R<font color='#5555FF'>*</font>x;
            matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>0</font>,<font color='#979000'>1</font><font color='#5555FF'>&gt;</font> tmp <font color='#5555FF'>=</font> R<font color='#5555FF'>*</font>x;
            R <font color='#5555FF'>=</font> l<font color='#5555FF'>*</font>R <font color='#5555FF'>-</font> l<font color='#5555FF'>*</font>l<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>tmp<font color='#5555FF'>*</font><font color='#BB00BB'>trans</font><font face='Lucida Console'>(</font>tmp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font><font color='#5555FF'>/</font>temp;

            <font color='#009900'>// Since we multiplied by the forget factor, we need to add (1-forget_factor) of the
</font>            <font color='#009900'>// identity matrix back in to keep the regularization alive.  
</font>            <font color='#BB00BB'>add_eye_to_inv</font><font face='Lucida Console'>(</font>R, <font face='Lucida Console'>(</font><font color='#979000'>1</font><font color='#5555FF'>-</font>forget_factor<font face='Lucida Console'>)</font><font color='#5555FF'>/</font>C<font face='Lucida Console'>)</font>;

            <font color='#009900'>// R should always be symmetric.  This line improves numeric stability of this algorithm.
</font>            R <font color='#5555FF'>=</font> <font color='#979000'>0.5</font><font color='#5555FF'>*</font><font face='Lucida Console'>(</font>R <font color='#5555FF'>+</font> <font color='#BB00BB'>trans</font><font face='Lucida Console'>(</font>R<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;

            w <font color='#5555FF'>=</font> w <font color='#5555FF'>+</font> R<font color='#5555FF'>*</font>x<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>y <font color='#5555FF'>-</font> <font color='#BB00BB'>trans</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font><font color='#5555FF'>*</font>w<font face='Lucida Console'>)</font>;

        <b>}</b>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>0</font>,<font color='#979000'>1</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_w'></a>get_w</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
        <b>{</b>
            <font color='#0000FF'>return</font> w;
        <b>}</b>

        <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> EXP<font color='#5555FF'>&gt;</font>
        <font color='#0000FF'><u>double</u></font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> matrix_exp<font color='#5555FF'>&lt;</font>EXP<font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> x
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
        <b>{</b>
            <font color='#009900'>// make sure requires clause is not broken
</font>            <font color='#BB00BB'>DLIB_ASSERT</font><font face='Lucida Console'>(</font><font color='#BB00BB'>is_col_vector</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font> <font color='#5555FF'>&amp;</font><font color='#5555FF'>&amp;</font> <font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>,
                "<font color='#CC0000'>\t double rls::operator()()</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t invalid arguments were given to this function</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t is_col_vector(x): </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#BB00BB'>is_col_vector</font><font face='Lucida Console'>(</font>x<font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t x.size():         </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> x.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t get_w().size():   </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t this: </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#0000FF'>this</font>
                <font face='Lucida Console'>)</font>;

            <font color='#0000FF'>return</font> <font color='#BB00BB'>dot</font><font face='Lucida Console'>(</font>x,w<font face='Lucida Console'>)</font>;
        <b>}</b>

        decision_function<font color='#5555FF'>&lt;</font>linear_kernel<font color='#5555FF'>&lt;</font>matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>0</font>,<font color='#979000'>1</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font> <b><a name='get_decision_function'></a>get_decision_function</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
        <b>{</b>
            <font color='#009900'>// make sure requires clause is not broken
</font>            <font color='#BB00BB'>DLIB_ASSERT</font><font face='Lucida Console'>(</font><font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font>,
                "<font color='#CC0000'>\t decision_function rls::get_decision_function()</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t invalid arguments were given to this function</font>"
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t get_w().size():   </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#BB00BB'>get_w</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> 
                <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> "<font color='#CC0000'>\n\t this: </font>" <font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font color='#0000FF'>this</font>
                <font face='Lucida Console'>)</font>;

            decision_function<font color='#5555FF'>&lt;</font>linear_kernel<font color='#5555FF'>&lt;</font>matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>0</font>,<font color='#979000'>1</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font> df;
            df.alpha.<font color='#BB00BB'>set_size</font><font face='Lucida Console'>(</font><font color='#979000'>1</font><font face='Lucida Console'>)</font>;
            df.basis_vectors.<font color='#BB00BB'>set_size</font><font face='Lucida Console'>(</font><font color='#979000'>1</font><font face='Lucida Console'>)</font>;
            df.b <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
            df.alpha <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
            df.<font color='#BB00BB'>basis_vectors</font><font face='Lucida Console'>(</font><font color='#979000'>0</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> w;

            <font color='#0000FF'>return</font> df;
        <b>}</b>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>inline</font> <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b><font face='Lucida Console'>(</font><font color='#0000FF'>const</font> rls<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>
        <b>{</b>
            <font color='#0000FF'><u>int</u></font> version <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
            <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>version, out<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.w, out<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.R, out<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.C, out<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.forget_factor, out<font face='Lucida Console'>)</font>;
        <b>}</b>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>inline</font> <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b><font face='Lucida Console'>(</font>rls<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>
        <b>{</b>
            <font color='#0000FF'><u>int</u></font> version <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
            <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>version, in<font face='Lucida Console'>)</font>;
            <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>version <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
                <font color='#0000FF'>throw</font> dlib::<font color='#BB00BB'>serialization_error</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>Unknown version number found while deserializing rls object.</font>"<font face='Lucida Console'>)</font>;

            <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.w, in<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.R, in<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.C, in<font face='Lucida Console'>)</font>;
            <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.forget_factor, in<font face='Lucida Console'>)</font>;
        <b>}</b>

    <font color='#0000FF'>private</font>:

        <font color='#0000FF'><u>void</u></font> <b><a name='add_eye_to_inv'></a>add_eye_to_inv</b><font face='Lucida Console'>(</font>
            matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> m,
            <font color='#0000FF'><u>double</u></font> C
        <font face='Lucida Console'>)</font>
        <font color='#009900'>/*!
            ensures
                - Let m == inv(M)
                - this function returns inv(M + C*identity_matrix&lt;double&gt;(m.nr()))
        !*/</font>
        <b>{</b>
            <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>long</u></font> r <font color='#5555FF'>=</font> <font color='#979000'>0</font>; r <font color='#5555FF'>&lt;</font> m.<font color='#BB00BB'>nr</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>r<font face='Lucida Console'>)</font>
            <b>{</b>
                m <font color='#5555FF'>=</font> m <font color='#5555FF'>-</font> <font color='#BB00BB'>colm</font><font face='Lucida Console'>(</font>m,r<font face='Lucida Console'>)</font><font color='#5555FF'>*</font><font color='#BB00BB'>trans</font><font face='Lucida Console'>(</font><font color='#BB00BB'>colm</font><font face='Lucida Console'>(</font>m,r<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font><font color='#5555FF'>/</font><font face='Lucida Console'>(</font><font color='#979000'>1</font><font color='#5555FF'>/</font>C <font color='#5555FF'>+</font> <font color='#BB00BB'>m</font><font face='Lucida Console'>(</font>r,r<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;
            <b>}</b>
        <b>}</b>


        matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>0</font>,<font color='#979000'>1</font><font color='#5555FF'>&gt;</font> w;
        matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font> R;
        <font color='#0000FF'><u>double</u></font> C;
        <font color='#0000FF'><u>double</u></font> forget_factor;
    <b>}</b>;

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<b>}</b>

<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_RLs_Hh_
</font>

</pre></body></html>